Sample-Efficient Piecewise Quadratic Regression Tree
Date Issued
2009
Date
2009
Author(s)
Chen, Chien-Ming
Abstract
The classification and regression tree (CART) is a popular method in data mining. It classifies the responses by sequentially splitting the sample into two branches. In CART, the sample size will deplete quickly and the reliability of prediction will diminish with splitting sample. Therefore, the sample efficient regression tree (SERT) is proposed. It uses interaction effect test to avoid unnecessary splits. However, CART and SERT can not detect the quadratic effect. For this reason, we propose the sample-efficient piecewise quadratic regression tree to solve the problem.irst we develop the piecewise quadratic regression model to detect the quadratic effect. Then, we use the Gram-Schmidt to resolve the possible multicollinearity issue between the linear effect and the quadratic effect. With this process, we can avoid wrong attribute selection resulted from statistical insignificance due to collinearity between the linear effect and the quadratic effect.inally, we use seventeen simulated cases and a real case to verify our proposed method.
Subjects
quadratic effects
regression tree
multiple regression
Gram-Schmidt Process
collinearity
Type
thesis
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